Perspective functions have long been used to convert fractional programs into convex programs. More recently, they have been used to form tight relaxations of mixed-integer nonlinear programs with so-called indicator variables. Motivated by a practical application (maximising energy efficiency in an OFDMA system), we consider problems that have a fractional objective and indicator variables simultaneously. To obtain a tight relaxation of such problems, one must consider what we call a “bi-perspective” (Bi-P) function. An analysis of Bi-P functions leads to the derivation of a new kind of cutting planes, which we call “Bi-P-cuts”. Computational results indicate that Bi-P-cuts typically close a substantial proportion of the integrality gap.
Eventually published as: A.N. Letchford, Q. Ni & Z. Zhong (2021) Bi-perspective functions for mixed-integer fractional programs with indicator variables. Math. Program., 190(1-2), 39-55.